Find the second Taylor polynomial P2(x) for the function f (x) = ex cos x about x0 = 0. a. Use P2(0.5) to approximate f (0.5). Find an upper bound for error |f (0.5) − P2(0.5)| using the error formula, and compare it to the actual error. b. Find a bound for the error |f (x) − P2(x)| in using P2(x) to approximate f (x) on the interval [0, 1]. c. Approximate 1 0 f (x) dx using 1 0 P2(x) dx. d. Find an upper bound for the error in (c) using 1 0 |R2(x) dx|, and compare the bound to the actual error.